BACKGROUND ART
Piezoelectric materials have become more and more widely used in a large number of applications. For example, piezoelectric materials have the potential of allowing aircraft designers to minimize the number of required moving parts with high precision as well as increased compactness. Conventional piezoelectric materials, however, generally only work well in applications that require micro-displacement such as adaptive optics, printer jet control, pressure and acoustic transducers, etc. It is therefore desirable to provide a system and method which is readily adaptable to large displacement or stroke applications under high loads. Such a system would gain widespread acceptance in the aviation industry.
Due to the limited strain capability (i.e. elongation per unit voltage input) of piezoelectric materials, a number of piezoelectric segments are typically fixedly coupled or glued together to obtain a useful displacement (or stroke). As the displacement requirements increase, the "column" of piezoelectric material becomes longer. If the piezoelectric material column were made several widths long (or diameters high), when subjected to an axial force due to a load, the column could become laterally (or radially) unstable. Lateral buckling could therefore occur and the column could collapse. Moreover, higher performance piezoelectric materials have a lower elastic modulus. For example, PI piezoelectric stack material has 1649 micro strain output with an elastic modulus of 4.1 lb/in.sup.4. In comparison, single Cr piezoelectric stack material has a higher strain output, 4718 micro strain, but an elastic modulus of only 1.5 lb/in.sup.4. It is therefore desirable to provide a method and apparatus that will provide support to the stack and delay buckling when the piezoelectric material strength alone is not sufficient to handle the applied load.
Recent approaches have attempted to make use of the fact that midpoint support of the piezoelectric stack allows the use of shorter piezoelectric columns. For a pin-ended piezoelectric stack the critical buckling load is: EQU Pcr=(.pi..sup.2 EI)/(Le.sup.2)
Where E is the elastic modulus of the column material, I is the minimum moment of inertia of the column cross-section, and Le is the effective length of the column or distance from pin joint to pin joint (See A. C. Ugural S. K. Foster, Advanced Strength and Applied Elasticity, page 332 equation 11.3, incorporated herein by reference).
The bucking load of any column may therefore be increased by adding restraints along the length of the column, thereby reducing the effective length of the column. The most effective approach is to put an additional support in the middle of the column, thereby minimizing the distance between any two adjacent pin supports. This approach cuts the effective length in half, and hence quadruples the critical buckling load.
Under conventional approaches to reduce the effective column length, however, piezoelectric expansion or contraction will cause the midpoint support to rotate and introduce lateral motion. The piezoelectric displacement in the axial direction will be reduced due to the rotation and resulting lateral displacement of the piezoelectric stack. In addition, as the midpoint support rotates, the axial compression load will be uneven over the cross-sectional area, and the axial force will set up internal bending moments at various points of the piezoelectric column. Therefore, conventional midpoint supports require the use of end caps to minimize the bending moment. The total axial displacement will be further reduced, however, due to the end cap compliance and Hertzian losses. Hertzian losses result from application of a force over a point or over a line as opposed to over a plane. The reduced surface area associated with end cap compliance therefore ultimately reduces transfer of the force from the stack to the load. The conventional midpoint support also mounts on to the structure base, and any relative base motion between the structure base and the column ends is directly translated into piezoelectric performance loss. It is therefore desirable to provide intermediate support to a piezoelectric stack which is not subject to rotation, bending moments, end cap compliance, or Hertzian losses.